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Set theory is the branch o mathematical logic that studies sets, which are collections o objects. This page wis last eeditit on 12 Mey 2019, at 16:42. Text is ...
Set theory. Statement. The intersection of and is the set of elements that lie in both set and set . Symbolic statement. In set theory, the intersection of two sets and denoted by [1] is the set containing all elements of that also belong to or equivalently, all elements of that also belong to [2]
Morse–Kelley set theory is named after mathematicians John L. Kelley and Anthony Morse and was first set out by Wang (1949) and later in an appendix to Kelley's textbook General Topology (1955), a graduate level introduction to topology. Kelley said the system in his book was a variant of the systems due to Thoralf Skolem and Morse.
In the foundations of mathematics, von Neumann–Bernays–Gödel set theory ( NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces the notion of class, which is a collection of sets defined by a formula whose quantifiers range only over sets.
Naïve set theory defines a set as any well-defined collection of distinct elements, but problems arise from the vagueness of the term well-defined. Axiomatic set theory [ edit ] In subsequent efforts to resolve these paradoxes since the time of the original formulation of naïve set theory, the properties of sets have been defined by axioms .
Descriptive set theory begins with the study of Polish spaces and their Borel sets . A Polish space is a second-countable topological space that is metrizable with a complete metric. Heuristically, it is a complete separable metric space whose metric has been "forgotten". Examples include the real line , the Baire space , the Cantor space , and ...
See also Naive set theory for the mathematical topic. First edition. Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory. [1] Originally published by Van Nostrand in 1960, [2] it was reprinted in the Springer-Verlag Undergraduate Texts in Mathematics series in 1974.
